10. Correct. The answer is false. The moment generating function is:
Provided that | t | < 2, the result above is 1/(1-t/2). This result is the infinite sum of the following series:
But, the general formula of M(t) is:
Thus, by comparing the terms between the series we have that:
E[X] = 1/2 (equivalent to 500 barrels per day) and E[X2] = 1/2
The variance is: σ2 = E[X2] - E[X]2 = 1/4 . The standard deviation is: (1/4)0.5 = 1/2.
The expected oil production level is 500 barrels per day and its standard deviation is 500 barrels per day. The expected oil production is not enough to break even, for it is not convenient to exploit the oil well.